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What happens if the load on the electrical generator exceeds its power generation? and why?

To be more precise, suppose we have a standard induction generator operating at frequency $\nu=50\:\mathrm{Hz}$ and voltage $V_0$, and rated to produce a maximum power $P_0$, and that we connect this to a load $R<V_0^2/P_0$, which will try to draw more power than the generator's capacity. Obviously the details will depend on the type of generator, but, generally speaking: what will be the generator's response, and what physical processes are involved?

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As the current drawn by the load increases the torque opposing the motion of the prime mover on its coils increase. This opposing torque is a result of the force acting on the coil since it's a current carrying conductor moving in a magnetic field. Hence its rpm reduces and so does its voltage output.

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The generator circuit breaker should trip to avoid damage. But if that doesn't work, or doesn't exist, the generator will not be able to maintain its speed. On a typical AC system, this will cause the frequency to drop from the standard 50 or 60 Hz, as well as drop the output voltage.

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If the generator's power source exceeds the generator's capacity, and if a load is placed on the generator that also exceeds the generator's capacity, and if all safety devices are disabled; the generator would heated up to a point where the weakest link would burn out like a fuse and thus remove the electrical load.

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just decelerates and finally stops because of heat-induced physical deformations; because the load is always against the power of the engine. The engine always has limited work ability because of limited energy and so power.

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